## Research Seminars in the School of Mathematical Sciences

The School of Mathematical Sciences host regular research seminars delivered by internal and external researchers on topics across mathematical sciences. Seminars take place on the Kevin Street campus and are open to all.

## Seminar 31/03/17: Modelling of the stratified flow circulation in Greenland fjords

Modelling of the stratified flow circulation in Greenland fjords

Violeta Moloney

Swansea University

Friday 31 March 2017

2pm, Room KE2-008, 2nd Floor, Main Building, DIT Kevin Street

Abstract:

The glacier/fjord/ocean is a unique complex system. The seasonal changes in atmospheric temperatures and constant interaction with ambient waters affect the salinity and temperature balance in the fjords and that has an impact on the glacier melt rate. The subject of investigation is the physical processes in Sermilik Fjord, Greenland.

This research investigates the effects of the subglacial discharge, Coriolis force, wind and tidal forcing on the stratification and circulation in the fjord using the three-dimensional model TELEMAC-3D. Firstly, in order to avoid large horizontal pressure gradients at an open boundary, the matching conditions for temperature and salinity between coastal and fjord domains had to be found before the other forces such as wind, tide and fresh water discharge were applied. Secondly, measured wind speed, tidal levels and velocities, and a representation of the subglacial discharge have been implemented to reproduce an analysis of seasonal conditions. After calibration, the tidal model produced matching results with the measured tides. The tidal analysis shows that the strength and direction of the tidal currents are sensitive to any changes in the width and shape of the domain. The effect of Coriolis force, the wind stress and the tidal propagation has been shown to play an important role on the fjord circulation, and particularly the stratification. However, the wind forcing has the strongest effect on the velocities, temperature and salinity profiles through the water column. The addition of the subglacial discharge has produced the turbulent flow that affects stratification near the glacier front, but it has little effect on the fjord dynamics further away from the source. When all forces are combined the winter conditions have shown the biggest changes in the fjord dynamics, as strong winds drive the circulation in fjord and that in turn delivers the coastal waters to the glacier.

## Seminar 9/12/16: Maths behind bars

Maths behind bars

Catherine Byrne

Dublin Institute of Technology

Friday 9 December 2016

1pm, Blue Room, DIT Kevin Street

Abstract:

The field of prison mathematics education is a relatively new research area. Mathematics is now a compulsory component of every full award in Further Education at all levels including prison education centres, where the most popular levels are QQI (formerly FETAC) level 2 and 3. There is a need to assess the mathematical level of people who are starting back to education. To see the impact of education on these students, it was essential to have a test at the point of entry to the education centre. This research examined the results gathered over several years, of 440 people who sat a locally devised test. The test was devised by prison teachers for this context and the outcomes were comparable with national and international assessment frameworks. It shows the numbers of people whose skills matched each level, (from pre-literacy, level 1, level 2 and level 3), the maths competencies that were weakest and needed most assistance and the types of skills which had been acquired through the everyday life and activities of the student.

These results will enable us to target mathematics support in the areas that need it most, and will enable more people to progress on the ladder of learning. The results of this research will have an impact on the future development of basic education assessment in this context, and in the wider field of adult basic education. This project aims to develop a wider assessment framework that will give a clear picture of the mathematical competencies, attitudes to mathematics and mathematical self-efficacy that is culturally appropriate. The research will give data on the impact of learning mathematics in prison and on desistance.

Biography:

Catherine Byrne is a teacher of ten years’ experience in Cloverhill Remand Prison and a teacher in special and prison education for thirty-five years. She is engaged in research for a PhD on Mathematics Education in Dublin Institute of Technology (DIT).

## Seminar 11/03/16: Dynamics of internal wave-current interaction

Dynamics of internal wave-current interaction

Alan Compelli

Dublin Institute of Technology

Friday 11 March 2016

2.30pm, Blue Room, DIT Kevin Street

Abstract:

A bounded system consisting of two fluids is considered. An internal wave, driven by gravity, acts as a free common interface between the fluids. Various current profiles are examined. A Hamiltonian formulation is taken and the resultant equations of motion show that wave-current interaction is not influenced by the current profile outside of the strip adjacent to the internal wave.

## Seminar 21/10/16: Noise and dissipation on coadjoint orbits

Noise and dissipation on coadjoint orbits

Alexis Arnaudon

Imperial College London

Friday 21 October 2016

1pm, Blue Room, DIT Kevin Street

Abstract:

In this talk I will start by introducing a stochastic perturbation of mechanical systems with symmetries that is most compatible with the preservation of geometrical invariants, or conserved quantities. In order for interesting phenomenons to emerge in these systems, I will add a dissipative term that also preserves the geometrical structure of the equations. Having both noise and dissipation in these systems will allow me to make a thermodynamical interpretation of the expected solutions and introduce a notion of temperature. Another feature is the existence of the so-called random attractors, a building block in modern random dynamical systems theory, that I will present in some details, with helps of some numerical simulations. My main examples of such systems will be the free rigid body associated to the group of rotations, and the heavy top when this symmetry is broken and requires the theory of semi-direct products. I will discuss some numerical challenges associated to these stochastic processes, and, if time permits, another application of this methodology to landmark dynamics in image matching.

This is joint work with D. Holm and A. De Castro and is an arXiv paper with number 1601.02249

## Seminar 12/02/16: Ways of Seeing Julia Sets: Visualizing the forces that shape fractal Julia sets

Ways of Seeing Julia Sets: Visualizing the forces that shape fractal Julia sets

Ted Burke

School of Electrical and Electronic Engineering, DIT

Friday 12 February 2016

1pm, Blue Room, DIT Kevin Street

Abstract:

Early in the 20th century, work by mathematicians such as Pierre Fatou and Gaston Julia on complex dynamics led to the definition of so-called Julia sets. When a rational complex polynomial function is applied iteratively to a complex number, z, it produces a sequence of complex values called the orbit of z. Depending on the particular function and on the value of z, that orbit may or may not remain bounded. For a given function, the Julia set forms the boundary between those regions of the complex plane where the orbits remain bounded and those where they do not.

Intriguingly, even for quite simple iterative complex functions, Julia sets often take on very striking fractal shapes. With the aid of a computer, it is easy to visualize the Julia set of a function but, for most people, understanding why it takes on a fractal shape is difficult. In my own ongoing struggle to gain a more intuitive understanding of fractals, I have written many short computer programs to visualize them in different ways. In this presentation, I will explore some ways of visualizing Julia sets which I found helpful in understanding why they are fractal.